This invention relates to position controls.
In control systems, there is a class of control problems that exhibit velocity limits that change independently of the position controller. Electro-mechanical position controllers use motors that have an inherent velocity limit in the back EMF of the motor verses the supplied voltage to the system. As the supply voltage varies the velocity limit of the system varies.
Hydraulic systems are limited by the pump characteristics and other loads on the hydraulic pump when the actuator is operated. In a single gimbal control moment gyroscope (CMG) controlled satellite application, the velocity limit becomes the available angular momentum from the CMG array.
The problem with a velocity limit force limited system is that there is inconsistent performance when the velocity limit changes. Using a linear control results in good performance with a low velocity limit but a system that overshoots if there is are high velocity limit. Conversely, good performance with a high velocity limit introduces a longer settling time than a smaller velocity limit. Conversely, good performance with a high velocity limit and produces a long settling time with a smaller velocity limit.
FIG. 1 exemplifies the prior art and the limit problem- A controller 10 provides a position command Xc which is summed with the velocity and position of an object or xe2x80x9cmassxe2x80x9d 12. A force limited actuator 14, such as a CMG, is controlled by the position there are 16 and moves in the mass 12. The function 18 represents the inherent actuator force limit as a function of input position error at 16. The function 18 output is effectively summed with a velocity limit VL from a velocity limit 11 for the actuator, such as a power supply limit or CMG angular momentum saturation. The actuator has inherent feedback and transfer characteristics 14a-d, in addition to the force limitation that is represented by transfer function 18. The performance of this system for a small 0.1 inch step in Xc (commanded position) followed by a large 2.4 inch step to 2.5 inches would show that for the small step the mass moves precisely with no overshoot because the velocity limit of the actuator is not reached. However, for the large step the system is limited by velocity limit, which results in a large overshoot and ringing.
Following classic control theory, two approaches have been used on this common problem. One centers on finding a compromise set of gains that give good performance with some intermediate velocity limit with some modest over shoot at high velocity limits and some long tails (decay or settling time) at low velocity limits. This solution works well if the variation in the velocity limit is not very large. A second approach pre-calculates a new set of gains for each transient but suffers from miscalculation when the initial and actual conditions are different, for instance a second position change is commanded during a transient. The controller can be confused by this change and produce incorrect gains. For that reason, this gain solution is not widely used.